Studying online (if an online offering is shown below)
There are now 2 possible online modes for units:
Units with modes Online timetabled and Online flexible are available for any student to self-enrol and study online.
Click on an offering mode for more details.
Unit Overview
- Description
This unit covers topics from differential topology, calculus on manifolds and differential geometry according to student background and needs. The topics may include integral curves of vector fields, differential forms, Lie brackets, integration on manifolds and Stokes' theorem, De Rham cohomologies, the Laplace-Beltrami operator on manifolds, the Hodge star operator, curves in Euclidean spaces, Frenet formulae, global properties of curvature, curvatures of surfaces in 3-space, Riemannian metrics, covariant differentiation, geodesics, applications in mechanics and electromagnetism.
The actual topics covered may vary from year to year depending on student demand and lecturer availability.
- Credit
- 6 points
- Offering
Availability Location Mode Not available in 2026 UWA (Perth) On-campus -
The timetable for this teaching period is not currently available. Please see the Important Dates page for the timetable release date and other key date information.
- Details for undergraduate courses
- Honours option in Mathematics; Statistics [Bachelor of Science (Honours)]
- Outcomes
Students are able to (1) develop mathematical ideas and the ability to articulate these ideas within a formalism at an appropriate level; (2) use tools for solving analytical problems of physics and engineering with geometric constraints; and (3) prove results about calculus on manifolds and differential geometry and construct examples demonstrating key concepts.
- Assessment
Indicative assessments in this unit are as follows: (1) test; (2) assignments; and (3) exam. Further information is available in the unit outline.
Student may be offered supplementary assessment in this unit if they meet the eligibility criteria.
- Unit Coordinator(s)
- Giovanni Giacomin
- Unit rules
- Prerequisites
- Successful completion ofMATH3032 Topology and Analysis
- Contact hours
- 3 hours per week
- The availability of units in Semester 1, 2, etc. was correct at the time of publication but may be subject to change.
- All students are responsible for identifying when they need assistance to improve their academic learning, research, English language and numeracy skills; seeking out the services and resources available to help them; and applying what they learn. Students are encouraged to register for free online support through GETSmart; to help themselves to the extensive range of resources on UWA's STUDYSmarter website; and to participate in WRITESmart and (ma+hs)Smart drop-ins and workshops.
- Visit the Essential Textbooks website to see if any textbooks are required for this Unit. The website is updated regularly so content may change. Students are recommended to purchase Essential Textbooks, but a limited number of copies of all Essential Textbooks are held in the Library in print, and as an ebook where possible. Recommended readings for the unit can be accessed in Unit Readings directly through the Learning Management System (LMS).
- Contact hours provide an indication of the type and extent of in-class activities this unit may contain. The total amount of student work (including contact hours, assessment time, and self-study) will approximate 150 hours per 6 credit points.
Face to face
Predominantly face-to-face. On campus attendance required to complete this unit. May have accompanying resources online.
Online flexible
100% Online Unit. NO campus face-to-face attendance is required to complete this unit. All study requirements are online only. Unit is asynchronous delivery, with NO requirement for students to participate online at specific times.
Online timetabled
100% Online Unit. NO campus face-to-face attendance is required to complete this unit. All study requirements are online only. Unit includes some synchronous components, with a requirement for students to participate online at specific times.
Online Restricted
Not available for self-enrolment. Students access this mode by contacting their student office through AskUWA. 100% Online Unit.
NO campus face-to-face attendance. All study and assessment requirements are online only. Unit includes some timetabled activities, with a requirement for students to participate online at specific times. In exceptional cases (noted in the Handbook) students may be required to participate in face-to-face laboratory classes when a return to UWA’s Crawley campus becomes possible in order to be awarded a final grade.
External
No attendance or regular contact is required, and all study requirements are completed either via correspondence and/or online submission.
Off-campus
Regular attendance is not required, but student attends the institution face to face on an agreed schedule for purposes of supervision and/or instruction.
Multi-mode
Multiple modes of delivery. Unit includes a mix of online and on-campus study requirements. On campus attendance for some activities is required to complete this unit.